There are several formalisms for studying black hole thermodynamics.
The traditional formalism focuses on the initial establishment of the basic
laws of black hole thermodynamics and the calculation of thermodynamic quantities
[1]}, [2]}, [3]}, [4]}, [5]}. A relatively modern formalism
known as the extended phase space (EPS) formalism appeared about fifteen years ago
[6]}, which takes the negative cosmological constant
(hence only applicable to AdS black holes) as one
of the thermodynamic quantities (proportional to the pressure) and thus extended
the space of macro states. This formalism has attracted considerable interests
because it revealed various critical behaviors and the possible existence of
different types of phase transitions in black hole physics
[7]}, [8]}, [9]}, [10]}, , , , , , , [11]}, , , , , , , , , , , , , . In particular, the critical phenomena
of the charged spherically symmetric AdS black holes in conformal gravity,
whose weird behavior has largely triggered the motivation of the present work,
is analyzed in .
Further development of the EPS formalism includes the exploration of
black hole microstructures , , , the inclusion of the central charge and its conjugate
variable in the list of thermodynamic variables , , ,
which is inspired by the AdS/CFT correspondence, etc.
